document.write( "Question 121178: A driver sets out on a 20-mile trip. When he has gone halfway he finds he has averaged 25 mph. At what speed must he travel the rest of the way to make his overall average speed for the trip 40 mph? \n" ); document.write( "
Algebra.Com's Answer #88911 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
For this problem you use the formula that relates distance (D), rate of travel (R), and time (T).
\n" ); document.write( "The formula is:
\n" ); document.write( ".
\n" ); document.write( "D = R*T
\n" ); document.write( ".
\n" ); document.write( "[Think the distance I travel is equal to the rate (or speed) times the amount of time that I
\n" ); document.write( "travel at that speed. For example, the distance I cover at 50 miles per hour for 2 hours is 100
\n" ); document.write( "miles (50*2)]. You must use consistent units. If your speed is miles per hour, your time
\n" ); document.write( "must be in hours and the distance covered is in miles.
\n" ); document.write( ".
\n" ); document.write( "Now to the problem. The problem tells you that for the first half of the trip ... which is 10
\n" ); document.write( "miles ... the average rate is 25 mph. You know the distance (10) and the rate (25). The
\n" ); document.write( "question is how much time did this half of the trip take. Plug the information into the
\n" ); document.write( "distance equation and you have:
\n" ); document.write( ".
\n" ); document.write( "10 = 25*T
\n" ); document.write( ".
\n" ); document.write( "Solve for T by dividing both sides by 25 and you get:
\n" ); document.write( ".
\n" ); document.write( "T = 10/25 = 0.4 hours
\n" ); document.write( ".
\n" ); document.write( "So the driver has spent 4-tenths of an hour going the first 10 miles.
\n" ); document.write( ".
\n" ); document.write( "To average 40 mph and hour for the whole 20 miles, how much time does the trip involve? Plug
\n" ); document.write( "these numbers into the distance formula and you have:
\n" ); document.write( ".
\n" ); document.write( "20 = 40*T
\n" ); document.write( ".
\n" ); document.write( "Solve for T by dividing both sides of this equation by 40 and you get:
\n" ); document.write( ".
\n" ); document.write( "T = 20/40 = 0.5 hours
\n" ); document.write( ".
\n" ); document.write( "So to average 40 mph the driver must cover the 20 miles in 0.5 hours (a half hour). But
\n" ); document.write( "he has already used 0.4 hours to go the first 10 miles. That means that he will have to drive
\n" ); document.write( "the next 10 miles in the 0.1 hours remaining ... 0.5 minus 0.4 = 0.1 hours. Plug these two
\n" ); document.write( "values into the distance equation ... 10 miles and 0.1 hours and you have:
\n" ); document.write( ".
\n" ); document.write( "10 = R*(0.1)
\n" ); document.write( ".
\n" ); document.write( "Solve for the rate by dividing both sides of the equation by 0.1 and you get:
\n" ); document.write( ".
\n" ); document.write( "R = 10/0.1 = 100 miles per hour
\n" ); document.write( ".
\n" ); document.write( "So after going at 25 mph for the first half of a 20 mile trip, the driver must cover the
\n" ); document.write( "next half of the trip at 100 mph if the average speed for the trip is to be 40 mph.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to understand the problem.
\n" ); document.write( ".
\n" ); document.write( " \n" ); document.write( "
\n" );